A Biordered Set Representation of Regular Semigroups

✍ Scribed by Bing Jun Yu; Mang Xu

• Publisher: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• Year: 2005
• Tongue: English
• Weight: 231 KB
• Volume: 21
• Category: Article
• ISSN: 1439-7617
• DOI: 10.1007/s10114-004-0490-4

✦ Synopsis

In this paper, for an arbitrary regular biordered set E, by using biorder-isomorphisms between the ω-ideals of E, we construct a fundamental regular semigroup W E called NH-semigroup of E, whose idempotent biordered set is isomorphic to E. We prove further that W E can be used to give a new representation of general regular semigroups in the sense that, for any regular semigroup S with the idempotent biordered set isomorphic to E, there exists a homomorphism from S to W E whose kernel is the greatest idempotent-separating congruence on S and the image is a full symmetric subsemigroup of W E . Moreover, when E is a biordered set of a semilattice E 0 , W E is isomorphic to the Munn-semigroup T E 0 ; and when E is the biordered set of a band B, W E is isomorphic to the Hall-semigroup W B .